Partial Differential EquationsSpringer, 1982 - 249 páginas This book is a very well-accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy 's example of a linear equation without solutions. |
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... derivatives . We call u a solution of ( 1.1 ) if after substitution of u ( x , y , ... ) and its partial derivatives ( 1.1 ) is satisfied identically in x , y , ... in some region in the space of these independent variables . Unless the ...
... derivatives . We call u a solution of ( 1.1 ) if after substitution of u ( x , y , ... ) and its partial derivatives ( 1.1 ) is satisfied identically in x , y , ... in some region in the space of these independent variables . Unless the ...
Página 34
... derivatives of u on y . As a matter of fact , we can then also find successively the values of all higher derivatives of u on y , as far as they exist . We obtain , e.g. , three linear equations with determinant △ for uxxxuxxy , uxy by ...
... derivatives of u on y . As a matter of fact , we can then also find successively the values of all higher derivatives of u on y , as far as they exist . We obtain , e.g. , three linear equations with determinant △ for uxxxuxxy , uxy by ...
Página 57
... derivatives of order less than m can be given independently from each other ) . We are to find a solution u near S which has these Cauchy data on S. We call S noncharacteristic if we can get all Du for | a | = m on S from the linear ...
... derivatives of order less than m can be given independently from each other ) . We are to find a solution u near S which has these Cauchy data on S. We call S noncharacteristic if we can get all Du for | a | = m on S from the linear ...
Contenido
Chapter | 1 |
Quasilinear Equations | 9 |
The Cauchy Problem | 24 |
Derechos de autor | |
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Términos y frases comunes
assume ball boundary bounded uniformly Cauchy data Cauchy problem Cauchy sequence Cauchy-Kowalevski Chapter characteristic curves class C² coefficients compact support complex constant continuous converge defined denote derivatives of orders determined uniquely difference quotients Dirichlet problem domain of dependence elliptic exists follows formula Fourier function f(x fundamental solution Gårding given Green's identity heat equation hence Hint holds identity implies inequality initial data initial values initial-value problem integral surface Laplace equation Lemma linear matrix neighborhood non-characteristic norm obtained open set partial differential equation plane polynomial power series prescribed proof quasi-linear real numbers satisfies scalar second derivatives Show solved space square integrable sufficiently small test functions theorem u₁ vanish variables vector wave equation x₁ ΘΩ